Unified scaling law in the coherent noise model

The waiting time distribution between successive events and the unified scaling law is studied using the coherent noise model. It is shown that, although this model generates uncorrelated event sizes and does not exhibit criticality, it still provides the unified scaling law. We argue the role of characteristic kink observed in the unified scaling law and the meaning of the parameter C$C$ used to fix the peak of the kink to unity. Our results indicate that the parameter C$C$ is indeed a physical quantity localizing the end of the linear tendency in the scaling law, which corresponds to the completion of the dominance of correlated events in time.     

Correlations and variability in electrical signals related to earthquake activity

Evaluating complex fluctuations in geoelectric time series is an important task not only for earthquake prediction but also for understanding complex processes related to earthquake preparation. Previous studies have reported alterations, such as the emergence of correlated dynamics in geoelectric potentials prior to an important earthquake (EQ). However, the presence of correlations and its relation with variability has not been widely explored. In this work we apply the detrended fluctuation analysis and the multiscale entropy methods to analyze the fluctuations of geoelectric time series monitored in two sites located in Mexico. We systematically calculate the correlation exponents and the sample entropy (S_E) of geoelectric time series. Important differences in the scaling exponents and entropy profiles for several time scales are observed. In particular, a complex behavior, characterized by a high entropy across several scales and crossover in the correlation exponents, is observed in the vicinity of an that occurred on Sept. 14, 1995. Moreover, we compare the changes in the entropy of the original data with their corresponding shuffled version to see whether correlations in the original data are related to variability.     

Stochastic modeling for starting-time of phase evolution of random seismic ground motions

In response to the challenge inherent in classical high-dimensional models of random ground motions, a family of simulation methods for non-stationary seismic ground motions was developed previously through employing a wave-group propagation formulation with phase spectrum model built up on the frequency components' starting-time of phase evolution. The present paper aims at extending the formulation to the simulation of non-stationary random seismic ground motions. The ground motion records associated with N—S component of Northridge Earthquake at the type-II site are investigated. The frequency components' starting-time of phase evolution of is identified from the ground motion records, and is proved to admit the Gamma distribution through data fitting. Numerical results indicate that the simulated random ground motion features zero-mean, non-stationary, and non-Gaussian behaviors, and the phase spectrum model with only a few starting-times of phase evolution could come up with a sound contribution to the simulation.     

A preliminary study of post-seismic effects of radon following the Ms 8.0 Wenchuan earthquake

The observation data for radon from national geochemical observation points have been collected and analyzed following the Ms 8.0 Wenchuan earthquake on 12th May, 2008 and a post-seismic effect of radon was observed. It has provided the most abundant record since the radon observation network had been set up in china. In this paper, the behaviour of the post-seismic effects of radon gas and water radon is reported. The results were obtained that observation points recording post-seismic effects of radon release were distributed mainly along the extended line of Longmenshan faults, and located on the boundary faults of regional tectonic blocks (Category II) and inside some tectonic blocks (Category II). The pattern of variation in radon emission observed was largely in the form of rising steps. A comparison was made with the variation of water level and flow observed simultaneously with radon measurement, to investigate a dynamic link with post-seismic radon with underground water conditions. This study confirmed a response of radon concentration to the seismic wave, and also raised other scientific issues, such as the dynamic association between geochemical composition of underground water and medium parameter variation of aquifers under dynamic loading, which may support the study of the mechanism of earthquake precursors of radon.     

Earth surface effects on active faults: An eigenvalue asymptotic analysis

We study in this paper an eigenvalue problem (of Steklov type), modeling slow slip events (such as silent earthquakes, or earthquake nucleation phases) occurring on geological faults. We focus here on a half space formulation with traction free boundary condition: this simulates the earth surface where displacements take place and can be picked up by GPS measurements. We construct an appropriate functional framework attached to a formulation suitable for the half space setting. We perform an asymptotic analysis of the solution with respect to the depth of the fault. Starting from an integral representation for the displacement field, we prove that the differences between the eigenvalues and eigenfunctions attached to the half space problem and those attached to the free space problem, is of the order of d^-2, where d is a depth parameter: intuitively, this was expected as this is also the order of decay of the derivative of the Green's function for our problem. We actually prove faster decay in case of symmetric faults. For all faults, we rigorously obtain a very useful asymptotic formula for the surface displacement, whose dominant part involves a so called seismic moment. We also provide results pertaining to the analysis of the multiplicity of the first eigenvalue in the line segment fault case. Finally we explain how we derived our numerical method for solving for dislocations on faults in the half plane. It involves integral equations combining regular and Hadamard's hypersingular integration kernels.     

Direct Likelihood Evaluation for the Renewal Hawkes Process

An interesting extension of the widely applied Hawkes self-exiting point process, the renewal Hawkes (RHawkes) process, was recently proposed by Wheatley, Filimonov, and Sornette, which has the potential to significantly widen the application domains of the self-exciting point processes. However, they claimed that computation of the likelihood of the RHawkes process requires exponential time and therefore is practically impossible. They proposed two expectation–maximization (EM) type algorithms to compute the maximum likelihood estimator (MLE) of the model parameters. Because of the fundamental role of likelihood in statistical inference, a practically feasible method for likelihood evaluation is highly desirable. In this article, we provide an algorithm that evaluates the likelihood of the RHawkes process in quadratic time, a drastic improvement from the exponential time claimed by Wheatley, Filimonov, and Sornette. We demonstrate the superior performance of the resulting MLEs of the model relative to the EM estimators through simulations. We also present a computationally efficient procedure to calculate the Rosenblatt residuals of the process for goodness-of-fit assessment, and a simple yet efficient procedure for future event prediction. The proposed methodologies were applied on real data from seismology and finance. An R package implementing the proposed methodologies is included in the supplementary materials.     

Modeling of non-stationary ground motion using the mean reverting stochastic process

This paper presents a new method for modeling amplitude and frequency non-stationary earthquake ground motions using a scalar first order dynamic mean reverting stochastic differential equation driven by Brownian motion with parametric time varying coefficients. It determines the proper relationship between these time varying parametric coefficients and presents the statistical and probability distribution characteristics of the response solution. It demonstrates the applicability of the method by presenting some simulations of amplitude and frequency non-stationary earthquake ground motions. The verification of the amplitude and frequency non-stationary contents of the mean reverting stochastic ground motions is demonstrated using the Hilbert–Huang transform method. Also a corresponding interpretation between the coefficients of the proposed model and the coefficients of the usual oscillatory second order differential equation driven by white Gaussian noise is presented along with some comments how it can be applied to simulate ground motions consistent with acceleration target records such as boxcar, trapezoidal, other exponential functions, or compound and target records at source, near field, and far field distances.     

Active TLCGD control of plane asymmetric buildings under earthquake excitation

The sealed,tuned liquid column gas damper (TLCGD) with gas-spring effect extends the frequency range of application and efficiently increases the modal structural damping.Active tuned liquid column gas damper (ATLCGD) is developed for the vibration control of plane asymmetric buildings subjected to earthquake excitation,improving the performance of the passive control scheme.The active behaviour is obtained by adjusting the pressure at the end of the liquid column using a pressurised reservoir.The classical linear quadratic regulator (LQR) design is presented as a straightforward approach to optimal control.Numerical simulations indicate a significant vibration reduction of plane asymmetric buildings by active control within the strong motion of the dynamic response.     

Evaluation of the Kushida Method of short-term earthquake prediction

Kushida and Kushida found that FM radio waves from stations at distances over-the-horizon are received before earthquakes. Based on this finding, since the mid-1990’s, the Kushidas have been practicing “Earthquake Precursor Detection Experiment”. The performance of the Kushida method during 2000–2003 has been evaluated by checking their predictions against the actual seismicity. During the period, there were 92 Kushida predictions mentioning the possibility of M ≥ 5.5 event, whereas there were 49 M ≥ 5.5 earthquakes in the Japanese region. If the criteria for successful prediction are set as: the errors in date is less than one day, epicentral position is roughly within specified area, and error in M is less than 0.5, the success rate was 20% and the alarm rate was 12%. If we relax the criteria to: the errors in dates within 10 days, epicenter within additional 100 km of specified area and the magnitude error less than 1.0, the success rate was 40% and the alarm rate was 27%. These rates may look insufficient for a practical prediction method. Considering, however, the fact that no other short-term prediction has ever been made in Japan so far it is a significant achievement. Moreover, it was found that in almost all failed predictions, meaningful signals were detected although the interpretations were incorrect. This indicates that the method is promising provided further investigation is carried out. The same evaluation at the M ≥ 6.0 level showed that the general performance was similar to the M ≥ 5.5 level, except that both success rate and alarm rate were lower at the M ≥ 6.0 level. If this unexpected finding is real, it might be inherent to the methodology using scattering of short-wave length radio waves as suggested by M. Hayakawa and may contain important information in understanding the earthquake physics and LAI-coupling. The results of the present study indicate strongly that the earthquake prediction research using anomalous transmission of VHF FM radio waves should be enhanced in parallel with complementary research in other frequency ranges.